Consider $\vec{F}$, as the total force applied on the system, $U$ the potential energy of the existent field, and $\vec{Q}$ a non-conservative force.
We have that:
$$F_k=-\frac{\partial U}{\partial q_k}+Q_k.$$
The Lagrange's equations for this type of system are:
$$\frac{d}{dt}\frac{\partial L}{\partial \dot{q_k}}-\frac{\partial L}{\partial q_k}=Q_k.$$
I know the deduction of Lagrange's equation of a conservative system, but not for this one.
I want to deduce those equations using Hamilton's Principle. Could you show me their derivation, or advise me some links of interest?
